Density of Solids and Liquids
From Chemistry Teachers United
In this lab the density of a liquid and a solid are determined. The volume of the solid is determined by two methods: liquid displacement in a graduated cylinder, and measurement of the solid's dimensions using vernier calipers.
Contents |
General Outcomes
- Correctly use a graduated cylinder and vernier calipers.
- Use the terms associated with use of this equipment.
- Describe how the density of a liquid or a solid can be determined.
- Use significant figures correctly in calculating density.
- Understand that density is an intrinsic property.
- Use densities to predict whether an object will float or sink in a liquid.
Specific Objectives:
- Know the meaning of the terms tare, meniscus, parallax error, TC, and TD.
- Explain why temperature appears on graduated cylinders.
- Be able to read a vernier caliper.
- Given measurement data for a liquid and a solid, calculate the density of each to the correct number of significant figures.
- Given an experimental procedure for determining density and the set of data obtained, suggest how the number of significant digits in the density could be improved by modifying the experiment.
- Given the densities of several liquids and whether a solid sinks or floats in each liquid, give the density range of the solid.
Graduated cylinders
Several types of laboratory glassware can be used to measure the volume of a liquid. A beaker is convenient for crude measurement. Figure 1 shows a 100 mL beaker that has volume markings on it. These marks are typically only accurate to within plus or minus 5%. If volume needs to be measured more accurately, a graduated cylinder may be used, Figure 2.
Figure 1. A beaker is not very accurate for measuring volumes. Notice, below the 80 mL mark, is written “± 5%”.
Figure 2. 10 mL and 100 mL graduated cylinders.
A graduated cylinder is a cylinder with graduations, which are marks indicating volume. (Graduations are marks arranged by grade: first grade, second grade, etc. In this case, the grade represents volume.) A graduated cylinder often has a plastic “bumper guard” that keeps the graduated cylinder from breaking if it is knocked over. The bumper guard does no good if it is slid to the bottom of the cylinder. If the opening in the bumper guard is lined-up with the spout of the graduated cylinder, liquid can be poured from the cylinder and the markings on the cylinder can be read without moving the bumper guard.
Not all of the liquid in a graduated cylinder can be poured out, because some water sticks to the walls of the glass container. If a graduated cylinder has been calibrated so that the marks on it indicate the total volume of liquid that the cylinder contains, then the cylinder is labeled TC, for “to contain”, Figure 3. If the cylinder has been calibrated so that the marks indicate the volume that will be poured out, or delivered, then the cylinder is labeled TD, for “to deliver”. TC and TD are used on most volumetric glassware (glassware used for measuring liquid volumes). (Plastic containers may be labeled “TC/TD”, because water doesn’t stick to plastic, so everything a plastic container contains can be poured out.)
Figure 3. Close-up of graduated cylinders, showing “TC” and “TD”.
The volume within a graduated cylinder will vary slightly as the cylinder’s temperature varies, because glass expands when heated. Graduated cylinders are usually labeled with a temperature, such as 20°C, that is the temperature at which they are calibrated to be most accurate, Figure 3.
The surface of the water in a cylinder is curved because water is attracted to glass. This curved surface is called a meniscus, Figure 4. The liquid level in volumetric glassware is measured from the bottom of the meniscus.
 |  |  |
| Eye above meniscus | Eye level with meniscus | Eye below meniscus |
| | |
Figure 4. (Top) Three views of the same meniscus. Parallax error occurs the eye is not at the same level as the liquid. (Bottom) Schematic showing how the perceived liquid level depends on the level of the eye.
Because the meniscus is curved, the location of the bottom of the meniscus depends on whether the eye is above, below, or at the same level as the meniscus. The level of the meniscus is determined with the eye at the same level as the meniscus. If the eye is higher or lower than the meniscus, the observed value will be inaccurate. This error is called a parallax error (because the eye is not parallel to the bottom of the meniscus).
Often, the volume dispensed with a graduated cylinder does not need to be very accurate. However, in this lab accurate measurements are required, which means that the level of the liquid in the graduated cylinder must be accurately determined, or “read”. When making a measurement with the scale of an instrument, the last digit in the measurement is estimated by mentally dividing the distance between divisions on the scale into tenths. The volume of liquid contained in a 100 mL graduated cylinder having markings every milliliter could be reported to the tenths of a mL, as, for example, 57.3 mL. The volume in a 10 mL graduated cylinder with graduations every tenth of a milliliter could be reported to a hundredth of a mL, as, for example 8.74 mL. Reading the scale of a graduated cylinder to its highest precision is not easy, because it is difficult to see exactly where the bottom of the meniscus is. How should the volume of liquid in the graduated cylinder in Figure 4 be reported? (Answer are just before the pre-lab questions. A common mistake is to count up starting with 90; the correct value is less than 90 mL.)
Tare the balance
“Tare” means to set the electronic balance to read zero by pushing a button or bar on the balance. The balance is often tared with an empty container on it, so that the mass of material added to the container can be read directly from the balance, without having to mentally subtract the mass of the container.
Vernier Calipers
The volume of a solid may be calculated from its dimensions. The dimensions may be measured using vernier calipers, Figure 5.
Figure 5. Vernier calipers measuring the size of a penny. The expanded view shows the vernier scale.
These calipers have a vernier scale that provides a way to determine the last digit of a measurement. In Figure 6, the main scale (on the top) is calibrated in millimeters. The vernier scale (on the bottom) is formed by dividing the distance covered by 9 millimeters into 10 divisions. On the vernier scale, only one of the marks from 0 to 9 will line up with a mark on the main scale. The mark that lines up gives the last digit in the measurement.
Figure 6. A vernier caliper with the jaws closed should read zero.
The main scale is read using the zero of the vernier scale, Figure 7. In that figure, the zero mark is between 4 and 5 on the main scale, so the measurement is greater than 4 mm. On the vernier scale the mark for 2 lines up most closely with a mark on the main scale, so the measurement should be reported as 4.2 mm. This is reasonable, because the zero mark appears to be around 0.2 mm beyond the 4 on the main scale.
Figure 7. The last digit of a measurement is obtained from the vernier scale. Here, the last digit is 2, because the mark for 2 lines up most closely with a mark on the main scale.
Significant Figures
In this lab, significant figures determine the precision of the density that is reported. Density calculations will look something like this:
In this calculation the subtraction is, of course, done first, then the division. Use the significant figures rules for addition & subtraction to determine how many significant figures should be in the result of the subtraction, then use the multiplication & division significant figures rules to determine how many significant figures should be in the final result. How should the above result be reported? (Answer are just before the pre-lab questions.)
Caution: The liquid whose density will be determined may contain rubbing alcohol, also known as isopropanol. This liquid is poisonous if ingested (unlike small amounts of drinking alcohol, also known as ethanol). Also, rubbing alcohol is flammable, so it must not be used around open flames.
Answers to self-test questions:
Graduated cylinder reading: 88.2 mL
Density: 1.2 g/mL, because the subtraction has to be done first.
Pre-lab Questions (13 points)
1. (4 pts) Record the volume of this graduated cylinder to the highest precision that should be used, given the graduations it contains. (Read the level at the very bottom of the meniscus. Like a real graduated cylinder, it isn’t easy to determine that level.)
Grading: 1 pt for units; 1 pt for correct number of decimals; 2 pts for correct number.
[Instructor: delete three of the following four figures.]
- ____________
2. (4 pts) Record the distance measured by this vernier caliper to the correct number of significant figures.
Grading: 1 pt for units; 1 pt for correct number of decimals; 2 pts for correct number.
[Instructor: delete three of the following four figures.]
- ____________
3. (2 pts) What two hazards are associated with isopropanol (rubbing alcohol)?
[Instructor: select just one of these.]
4. (3 pts) What does tare mean?
4. (3 pts) What does parallax error mean?
4. (3 pts) What does TC mean?
4. (3 pts) What does TD mean?
4. (3 pts) What is the purpose of the plastic ring sometimes found on graduated cylinders?
Procedure
Grading: -1 pt for each number that lacks units. -3 pts for incorrect number of significant figures. -1 to -5 points for accuracy of the result. -2 pts for not showing the calculation of density or, when called for, volume. (Showing the calculation makes it easier to determine where errors occurred if the result is wrong.)
The precision of beakers and graduated cylinders
Obtain a 100 mL beaker that has graduations on the side. Fill the beaker up to the 80 mL mark with tap water. Then transfer that water to a 100 mL graduated cylinder. Record the volume of liquid in the graduated cylinder:
- Volume ___________________
Which do you think is more accurate, and why?
Use a 100 mL graduated cylinder to determine how much water the 100 mL beaker really holds (to the nearest mL).
- Volume ___________________
Density of a liquid
The density of a liquid will be determined three times, each time using a different volume.
Obtain a 10 mL graduated cylinder. Determine if the cylinder is of type TC or TD. The procedure to follow depends on type cylinder type.
- cylinder type ______
Cylinder type: TC
- The marks on this type of graduated cylinder show the volume the cylinder actually contains. The mass of this type of cylinder must be determined when it is completely dry.
- If the inside of the cylinder is dirty, rinse it with about 3 mL of the unknown density liquid containing food coloring, and dispose of this liquid in the waste container labeled “density liquid waste”. Completely dry the cylinder. To dry the inside, roll a strip of paper towel into a cylinder that will fit into the graduated cylinder.
Cylinder type: TD
- The marks on this type of graduated cylinder show the volume the cylinder will deliver. The mass of this type of cylinder must be determined when it is wet. Normally, this type of cylinder is filled to, say, the 6 mL mark, then the liquid is poured into a container. The result is a wet graduated cylinder and a container containing 6 mL of liquid. In this lab, the process is reversed: initially the graduated cylinder is wet, then liquid is added to it. Since the cylinder was initially wet, the volume of liquid added can be read directly from the graduations.
- Rinse the inside of the cylinder with about 3 mL of the unknown density liquid containing food coloring, and dispose of this liquid in the waste container labeled “density liquid waste”. Pour out as much of the liquid as possible, but do not dry the inside of the cylinder.
First determination: using about 2 mL
Tare a balance, then record the mass of the empty 10 mL graduated cylinder in the table, below. Add about 2 mL of the density liquid to the graduated cylinder.
“About” means the exact amount doesn’t matter. Don’t make any effort to get exactly 1 mL of the liquid. Anything between, say, 1.5 and 3 mL will work just fine. If you try to get exactly 2.0 mL, you are apt to introduce error by thinking “it isn’t exactly 2.0 mL, but it's close enough.”
Read the volume of the liquid to the nearest tenth of a mL (don’t round off to the nearest 0.5 mL). Record that volume. Weight and record the weight of the 10 mL graduated cylinder containing the liquid. (Note that in the data table the heavier mass is above the lighter mass, making it easier to subtract the two masses to get the mass of the liquid.) Determine the density (show this calculation). Record the density to the correct number of significant figures. The contents of the graduated cylinder may be poured into the waste container labeled “density liquid waste”.
| mass of 10 mL graduated cylinder plus liquid | _________ |
| mass of 10 mL graduated cylinder | _________ |
| mass of liquid | _________ |
| volume of liquid in graduated cylinder | _________ |
| density of liquid | _________ |
Second determination: Repeat the above procedure using about 5 mL of the density liquid. Record your data in the space below, using the same format as the first time. (Remember that “about” means don’t waste time trying to get exactly that amount.)
Third determination: Repeat using about 9 mL of the density liquid.
Which of your three measurements do you think is most accurate? Give a reason.
Is density an extrinsic or intrinsic property? (These terms are defined in your textbook.) __________________
What evidence does your determination of the density of a liquid provide to support this?
Density and Floating
At room temperature, what is the density of water to three significant figures? ________
If the density liquid were gently poured into water, would you expect the density liquid to sink or float or completely mix with water? ____________________
Attempt to get two layers—one colored, one colorless—by carefully pouring 5 mL of water into 5 mL of the liquid with food coloring in a 10 mL graduated cylinder. Dispose of the liquid in the container labeled “density liquid waste”. Then repeat the procedure, except this time add the density liquid to the water.
Are your results consistent with your prediction? _____
Based on your results, what is the relaton between floating and density?
Density of a solid
Obtain a cylinder of metal and record its identifying number. Weigh it on the balance.
- cylinder number __________________
- mass of cylinder __________________
Volume by water displacement
Fill a 100 mL graduated cylinder about half full with water. Record the volume as accurately as possible, and record it in the table, below. Tilt the graduated cylinder and let the metal cylinder slide down to the bottom.
Do this carefully; if the cylinder slides too quickly, it may knock the bottom out of the glass graduated cylinder. Also, if the cylinder slides down quickly, it will splash drops of water out of the graduated cylinder.
Read and record the total volume of the liquid and metal cylinder as accurately as possible. Calculate the density (show this calculation) and record the density to the correct number of significant figures.
| volume of liquid plus cylinder | _________ |
| volume of liquid in graduated cylinder | _________ |
| volume of cylinder | _________ |
| density of cylinder | _________ |
The instructor has put the densities of four metals on the board. Which metal is the cylinder made of? ___________________
Volume by calculation
The volume of a cylinder is hπr2, where h is the height of the cylinder and r is its radius. Use vernier calipers to measure the dimensions of the metal cylinder. Calculate the volume (show this calculation), then use that volume to calculate the density of the metal cylinder.
| height | _________ |
| diameter | _________ |
| volume of cylinder | _________ |
| density of cylinder | _________ |
Which density do you trust most, and why?
Post-lab Questions (12 points)
[Instructor: Pick just one of the following two questions, and, for that question, delete all but three of the data rows in the table.]
1. (3 pts) Gravity floatation has been investigated as a means of separating minerals at ore mines in South Africa. (http://www.ansti.org/volume/Lukomonapaper.pdf). Bromoform, CHBr3, has a density of 2.87 g/mL. In the following table, indicate which of the minerals would float and which would sink in bromoform.
| Mineral | Density / (g/mL) | Float (F) or Sink (S)? |
| Feldspar | 2.56-2.76 | _____ |
| Quartz | 2.6 | _____ |
| Calcite | 2.7 | _____ |
| Apatite | 3.2 | _____ |
| Magnetite | 5.17 | _____ |
1. (3 pts) Plastic recycling plants get many kinds of plastic. Some common plastics are shown in the table. (The number by the plastics is the number placed on the bottom of many plastic containers to identify the type of plastic.) One simple method of separating plastics involves “gravity floation”. In the table, indicate whether each type of plastic would sink or float in water.
| Plastic | Name | Density (g/mL) | Float (F) or Sink (S)? |
| PETE (1) | Polyethylene terephthalate | 1.39 | _____ |
| HDPE (2) | High density polyethylene | 0.95-0.97 | _____ |
| V or PVC (3) | Polyvinyl chloride | 1.18-1.65 | _____ |
| LDPE (4) | Low density polyethylene | 0.92-0.94 | _____ |
| PP (5) | Polypropylene | 0.90-0.91 | _____ |
| PS (6) | Polystyrene | 1.05-1.07 | _____ |
| PMA | Polymethylmethacrylate (Plexiglas) | 1.24 | _____ |
| Teflon | polytetrafluoroethylene | 2.2 | _____ |
2. (3 pts) A 250 mL beaker is completely filled with water. Is the volume of liquid it contains apt to be 250.0 mL? Give a reason.
[Instructor: Use just one version of the following two questions.]
3. (3 pts) A procedure says to "Add about 50 mL of an iron solution to a beaker." A 100 mL beaker with graduations is on the bench top, while a 100 mL graduated cylinder is in another room. Would it be OK to use the beaker to measure the 50 mL of iron solution? Give a reason.
3. (3 pts) Because a procedure said to "Add about 10 mL of water to a test tube," a student carefully measured 10.0 mL of water with a 10 mL graduated cylinder and transferred the water to a test tube. What did the student not understand about the directions?
4. (3 pts) A technician needs to determine the density of a liquid, so she puts about 8 mL of the liquid into a weighed 100 mL graduated cylinder, reads the volume from the cylinder, weighs the cylinder plus liquid to obtain the mass of the liquid, and calculates the density. How could she have improved the precision of the value of the density that was determined?
